MHD mixed convection in a lid-driven cavity filled by a nanofluid with sinusoidal temperature distribution on the both vertical walls using Buongiorno's nanofluid model

In the present contribution, a numerical investigation is presented to study Buongiorno's nanofluid model for MHD mixed convection of a lid-driven cavity filled with nanofluid. A sinusoidal temperature and nanoparticle volume fraction distributions on both vertical sides is considered where the horizontal walls are kept adiabatic. The cavity is permeated by an inclined uniform magnetic field and the effects of Brownian motion and thermophoresis are incorporated into the nanofluids model. An accurate collocated finite volume method is employed to discretize the governing partial differential equations after converting them to a non-dimensional form using a suitable transformation variables. Comparisons with previously published work are performed and excellent agreement is obtained. The computation is carried out for wide ranges of the Hartmann number Ha(0⩽Ha⩽100), buoyancy ratio Nr(0.1⩽Nr⩽1), thermophoresis number Nt(0.1⩽Nt⩽1), Brownian motion parameter Nb(0.1⩽Nb⩽1), Lewis number Le(1⩽Le⩽10), Prandtl number Pr(0.054⩽Pr⩽10), inclined magnetic field angle γ(0o⩽γ⩽3π/2), Amplitude ε(0⩽ε⩽1.5), phase angle ξ(0o⩽ξ⩽3π/4) and Richardson number Ri(0.001⩽Ri⩽100). The obtained results are presented in terms of the streamlines, isotherms and nanoparticles volume fraction contours as well as local Nusselt number. Results demonstrate that, the presence of an inclined magnetic filed in the flow region leads to lose the fluid movement. Also, the fluid flow is dominated by the movement of the upper wall in the case of the highest values of the buoyancy ratio.